Max Sauerbrey
Dr. · Postdoctoral Researcher
MPI MiS
Research profile
Max Sauerbrey is an applied stochastic analyst working on the rigorous analysis of real-world phenomena featuring randomness. His research centres on stochastic partial differential equations, fluid mechanics and Markov processes.
Research areas
Nonlinear PDEs · SPDEs · Stochastic Fluid Dynamics · Non-equilibrium Statistical Mechanics, Interacting Particle Systems and Fluctuating Hydrodynamics
Five research keywords
stochastic PDEs · fluid mechanics · Markov processes · regularity theory · qualitative properties
Contact and links
Academic links
Curriculum vitae
| Date | Appointment / education |
|---|---|
| 11/2024–present | Postdoctoral researcher, Max Planck Institute for Mathematics in the Sciences, Leipzig; mentors: Benjamin Gess and Felix Otto. |
| 11/2020–10/2024 | PhD in Mathematics, Delft University of Technology; advisor: Manuel Gnann; promotor: Mark Veraar. |
| 10/2019–03/2020 | Research assistant, Fraunhofer ITWM, Mathematics for Vehicle Engineering. |
| 09/2018–10/2020 | MSc Mathematics International, TU Kaiserslautern. |
| 10/2015–08/2018 | BSc Mathematics, TU Kaiserslautern. |
Publications
This catalogue contains all publications by the member, including work from before joining SAiS. Journal versions and preprints are maintained as one record per scientific work.
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Parabolic-hyperbolic splitting in support propagation for stochastic porous media equations
Preprint · arXiv:2609.11468 (2026). Max Sauerbrey and Joshua Utley study support propagation and waiting-time phenomena for stochastic porous media equations with conservative noise.
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The Schrödinger equation with fluctuating nonlinearity in the energy space
We study nonlinear Schrödinger equations with nonlinear Stratonovich noise in their energy space $H^1(\mathbb R^d;\mathbb C)$. By combining the stochastic Strichartz estimates derived in [Potential Anal. 41 (2014), pp.\ 269–315] with the approach from [Ann.\ Inst.\ H.\ Poincaré Phys.\ Théor.\…
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Finite speed of propagation and waiting time phenomena for stochastic porous media equations with nonlinear conservative noise
Starting from localized energy estimates, we prove finite speed of propagation for kinetic solutions to stochastic porous media equations with nonlinear conservative noise, the existence and uniqueness of which has recently been established. In particular, we propose a novel iteration technique which…
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The stochastic Keller–Segel system in critical spaces
Accepted / forthcoming · Oberwolfach Report for the seminar Stochastic Partial Differential Equations in Critical Spaces. We study stochastic, parabolic-parabolic Keller–Segel equations on the $d$-dimensional torus in scaling critical Besov spaces, for $d \geq 3$. Using stochastic maximal regularity estimates, we prove local well-posedness of the equation, i.e.,…
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Introduce thermal noise before discretizing, not afterwards!
Workshop report · Oberwolfach Reports 23(1), 803–806 (2026). Incorporating thermal noise before discretising a continuum model.
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The Incompressible Navier–Stokes–Fourier System with Thermal Noise
We establish a solution theory for the incompressible Navier–Stokes–Fourier system with thermal noise, posed on the three-dimensional torus. While in the incompressible deterministic setting the equation for the velocity can be solved independently of the temperature, the inclusion of the effects of…
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A stochastic flow approach to De Giorgi-Nash-Moser estimates for SPDEs with smooth transport noise
The celebrated De Giorgi-Nash-Moser theory ensures that solutions to uniformly elliptic or parabolic PDEs are bounded and Hölder continuous, even with merely bounded measurable coefficients. For parabolic SPDEs with transport noise, boundedness has recently been established, but Hölder continuity remains a key…
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Well-posedness of the stochastic thin-film equation with an interface potential
Published · Communications in Mathematical Physics 407, 158 (2026). We consider strictly positive solutions to a class of fourth-order conservative quasilinear SPDEs on the $d$-dimensional torus modeled after the stochastic thin-film equation. We prove local Lipschitz estimates in Bessel potential spaces…
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Solutions to the stochastic thin-film equation for the range of mobility exponents n∈(2,3)
Published · Stochastic PDE: Analysis and Computations 13, 1502–1557 (2025). Recently, many existence results for the stochastic thin-film equation were established in the case of a quadratic mobility exponent $n=2$, in which the noise term $\partial_x(u^\frac{n}{2}\mathcal{W})$ becomes linear. In the case of…
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Solutions to the stochastic thin-film equation for initial values with non-full support
Published · Transactions of the American Mathematical Society, 379 (2026) 4, pp. 2343-2383. The stochastic thin-film equation with mobility exponent $n\in [\frac{8}{3},3)$ on the one-dimensional torus with multiplicative Stratonovich noise is considered. We show that martingale solutions exist for non-negative initial values. This advances on…
Current SAiS projects
No current SAiS project assignment has been confirmed; information should be provided if applicable.
Talks and posters
Selected talks and posters: information to be provided by the member.
Teaching
| Period | Teaching activity |
|---|---|
| 2020–2024 | Exercise classes at TU Delft: Analysis 2, Fourier Analysis, Differential Geometry, and Spectral Theory for Operators and Semigroups. |
| 2016–2020 | Exercise classes at TU Kaiserslautern: Foundations of Mathematics 1, Introduction to Functional Analysis, and Functional Analysis. |